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arXiv:1001.0397 · Physical Review A

Decoherence as a signature of an excited-state quantum phase transition

Armando Relaño, J. M. Arias, J. Dukelsky, J. E. García-Ramos, P. Pérez-Fernández

Published Dec 16, 2008• 77 citations
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Abstract

We analyze the decoherence induced on a single qubit by the interaction with a two-level boson system with critical internal dynamics. We explore how the decoherence process is affected by the presence of quantum phase transitions in the environment. We conclude that the dynamics of the qubit changes dramatically when the environment passes through a continuous excited state quantum phase transition. If the system-environment coupling energy equals the energy at which the environment has a critical behavior, the decoherence induced on the qubit is maximal and the fidelity tends to zero with finite size scaling obeying a power law.

DOI
10.1103/physreva.78.060102

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We analyze the decoherence induced on a single qubit by the interaction with a two-level boson system with critical internal dynamics. We explore how the decoherence process is affected by the presence of quantum phase transitions in the environment. We conclude that the dynamics of the qubit changes dramatically when the environment passes through a continuous excited state quantum phase transition. If the system-environment coupling energy equals the energy at which the environment has a critical behavior, the decoherence induced on the qubit is maximal and the fidelity tends to zero with finite size scaling obeying a power law.
We analyze the decoherence induced on a single qubit by the interaction with a two-level boson system with critical internal dynamics.We explore how the decoherence process is affected by the presence of quantum phase transitions in the environment.We conclude that the dynamics of the qubit changes dramatically when the environment passes through a continuous excited state quantum phase transition.If the system-environment coupling energy equals the energy at which the environment has a critical behavior, the decoherence induced on the qubit is maximal and the fidelity tends to zero with finite size scaling obeying a power-law.
The decoherence induced on a single qubit by its interaction with the environment is studied. The environment is modeled as a scalar two-level boson system that can go through either first-order or continuous-excited-state quantum phase transitions, depending on the values of the control parameters. A mean-field method based on the Tamm-Damkoff approximation is worked out in order to understand the observed behavior of the decoherence. Only the continuous-excited-state phase transition produces a noticeable effect in the decoherence of the qubit. This is maximal when the system-environment coupling brings the environment to the critical point for the continuous phase transition. In this situation, the decoherence factor (or the fidelity) goes to zero with a finite-size scaling power law.
We study the decoherence properties of a two-level (qubit) system homogeneously coupled to an environmental many-body system at a quantum transition, considering both continuous and first-order quantum transitions. In particular, we consider a ddd-dimensional quantum Ising model as environment system. We study the dynamic of the qubit decoherence along the global quantum evolution starting from pure states of the qubit and the ground state of the environment system. This issue is discussed within dynamic finite-size scaling frameworks. We analyze the dynamic finite-size scaling of appropriate qubit-decoherence functions. At continuous quantum transitions, they develop power laws of the size of the environment system, with a substantial enhancement of the growth rate of the qubit decoherence with respect to the case in which the environment system is in normal noncritical conditions. The enhancement of the qubit decoherence growth rate appears much larger at first-order quantum transitions, leading to exponential laws when increasing the size of the environment system.
We investigate the influence of an excited-state quantum phase transition on the quantum-speed-limit time of an open quantum system. The system consists of a central qubit coupled to a spin environment modeled by a Lipkin-Meshkov-Glick Hamiltonian. We show that when the coupling between qubit and environment is such that the latter is located at the critical energy of the excited-state quantum phase transition, the qubit evolution shows a remarkable slowdown, marked by an abrupt peak in the quantum-speed-limit time. Interestingly, this slowdown at the excited-state quantum phase transition critical point is induced by the singular behavior of the qubit decoherence rate, being independent of the Markovian nature of the environment.
This paper analyzes the decoherence induced on a single qubit by the interaction with a spin chain with nontrivial internal dynamics (XYXYXY-type interactions). The aim of the paper is to study the existence and properties of the so-called universal regime, in which the decoherence time scale becomes independent of the strength of the coupling with the environment. It is shown that, although such a regime does exist, as previously established by Cucchietti et al. [Phys. Rev. A 75, 032337 (2007)], it is not a clear signature of a quantum phase transition in the environment. In fact, this kind of universality also exists in the absence of quantum phase transitions. A universal regime can be related to the existence of an energy scale separation between the Hamiltonian of the environment and the one characterizing the system-environment interaction. The results presented also indicate that in the strong-coupling regime the quantum phase transition does not produce an enhancement of decoherence (as opposed to what happens in the weak-coupling regime).